Assistant Professor Kosuke Nakano and Professor Ryo Maezono of the Japan Advanced Institute of Science and Technology (JAIST) announced the successful calculation of the lattice vibration (phonon dispersion) of a solid periodic system using the first-principles quantum Monte Carlo method via the software TurboRVB, for the first time in the world, in a joint project with Professor Sandro Sorella of the International School for Advanced Studies, Italy, and researcher Michele Casula and postdoc researcher Tommaso Morresi of Sorbonne Université (Sorbonne University), France. The achievement was published as a letter in the journal Physical Review B and chosen as the Editor’s Suggestion for its particular importance.

The Schrödinger equation is a basic method for explaining the electronic physical properties of matter. Methods used to calculate the Schrödinger equation without using experimental data are collectively called first-principles calculations. The most common type of first-principles calculation used today is based on Density Functional Theory (DFT), and it has been used successfully many times in the area of condensed-matter physics.

However, DFT comes with a major problem, which is that the outcome depends greatly on the exchange-correlation functional selected, and there was a need for a more accurate, next generation method to calculate electronic physical properties.

The first-principles quantum Monte Carlo method is a type of Monte Carlo method used to solve the many-body Schrödinger equation, which has been considered as a candidate for the next generation exact enumeration approach because the results do not depend on the exchange-correlation functional. However, even though the accurate energy value can be calculated using the first-principles quantum Monte Carlo method, the problem has remained for years that the derivative thereof (the energy by which atoms move) can not be easily determined. As a result, the applications of the method were limited because it was not possible to determine stable structures (structure optimization) or calculate lattice vibration (phonons) or free energy, which are important for materials development research.

The research group found that the problem of divergence of statistical error of the evaluation value of the energy of atoms moving in a solid periodic system under the first-principles quantum Monte Carlo method was due to the condition number of the overlap matrix of the basis functions, or in other words, the linear dependency between the basis functions. By then managing to eliminate the overlap between the basis functions, they succeeded in dramatically reducing the dispersal of the statistical error. The group also applied the method they had developed to a diamond, very commonly used as a reference material, and obtained a phonon dispersion that matched experimental values.

This revolutionary achievement greatly expands the scope of application for the first-principles quantum Monte Carlo method, that was hitherto limited, and enables the calculation of the lattice properties of materials that had previously been difficult to handle under computational materials science, with high precision.

The calculation using the first-principles quantum Monte Carlo method was carried out using the computational resources of the Fugaku super computer provided under the auspices of the JAIST large scale computers and HPCI system usage research topics. Going forward, the method will be applied in earnest to strongly correlated materials, previously difficult to handle using electronic state calculations, by leveraging the computational power of exascale super computers such as Fugaku to the maxium.

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